What exactly are the stakes?

I want to be careful how I frame this, partly because it's a big, complicated question and partly because it would be easy to imply an extreme position that I do not hold.

All that said, there's a thought that's been nagging at me for years, particularly since I've been digging into the education reform debate. Over the Twentieth Century, America has swung from one pedagogical and curricular extreme to another. The data from these initiatives are confusing and inconclusive when we look at the various metrics we use to capture educational performance, but when we pull back and look at two of the big objectives we want the policies to accomplish, economic growth.and technological progress, it's difficult to see a clear relationship between how and what we teach kids and how well they do.

This table (from A Brief History of American K-12 Mathematics Education in the 20th Century by David Klein) really brought this home for me. One of the big and not entirely unreasonable drivers of the reaction to Sputnik was the belief that we had been neglecting math and science.

Percentages of U.S. High School Students Enrolled in Various Courses

School Year	Algebra	Geometry	Trigonometry
1909 to 1910	56.9%	30.9%	1.9%
1914 to 1915	48.8%	26.5%	1.5%
1921 to 1922	40.2%	22.7%	1.5%
1927 to 1928	35.2%	19.8%	1.3%
1933 to 1934	30.4%	17.1%	1.3%
1948 to 1949	26.8%	12.8%	2.0%
1952 to 1953	24.6%	11.6%	1.7%
1954 to 1955	24.8%	11.4%	2.6%

It has become fairly standard to use the number of and enrollment in advanced course as a measure of a school's quality. By this standard, American schools weren't just bad, they were horrible and they had been in steady decline for half a century. Looking at the numbers for the Thirties and Forties, this generation would appear to be woefully ill-prepared to deal with the STEM-heavy world of the late Twentieth Century, but of course they weren't. The students who graduated high school in the quarter century preceding Sputnik were responsible for an incredible period of across-the-board advances.

From  Dewey Progressivism to New Math to Back-to-Basics to the modern reform movement, we have applied all sorts of theories to our kids' education. I'm sure that, if we thought through the problem, sharpened our analytic tools and devoted adequate resources to the question,  we could definitively say that for a given student and a given goal a certain approach is best.

I just wondering how big the magnitude of those differences will be compared to the impact of other public policy developments.